Understanding the state of cellular signaling systems provides insights to how cells behave under physiological and pathological conditions. Cellular signaling systems are organized as hierarchy (cascade) and signals of a molecular is often compositionally encoded to control cellular processes, such as gene expression. This project aims to develop advanced deep learning models (DLMs) to simulate cellular signaling systems based on gene expression data. In last 3 years, the project has made significant progresses, but the challenges remain. Importantly, contemporary DLMs behave as ?black boxes?, in that it is difficult to interpret how signals are encoded and how to interpret which signal a hidden node represent in a DLM. This black-box nature prevents researchers from gaining biological insights using DLMs, even though these models can be much superior in modeling data than other types of models in many tasks, e.g., predicting drug sensitivity of cancer cells. In this competitive renewal, we propose to develop novel DLMs and innovative inference algorithms to train ?interpretable? DLMs and apply them in translational research. The proposed research is innovative and of high significance in several perspectives: 1) Our novel DLMs and algorithms take advantage of big data resulting from systematic chemical/genetic perturbations of cellular signaling machinery, so that we can use the perturbation condition as side information to reveal how signals are encoded in a DLM. 2) We integrate principles of causal inference and information theory with deep learning method to make DLMs interpretable. As results, that researchers can gain mechanistic insights from such models. 3) Innovative application of interpretable DLMs will advance translational research. For example, we will train interpretable DLMs to model cellular signaling at the level of single cells and use this information investigate inter-cellular interactions among cells in tumor microenvironment to shed light on immune evasion mechanisms of cancers. We will also use information derived from interpretable DLMs to predict cancer cell drug sensitivity. We anticipate that our study will bring forth significant advances not only in deep learning methodology but also in precision medicine.